The lifespans of tigers in a particular zoo are normally distributed. The average tiger lives $25.7$ years; the standard deviation is $2.1$ years. Use the empirical rule (68-95-99.7%) to estimate the probability of a tiger living between $23.6$ and $29.9$ years.
$25.7$ $23.6$ $27.8$ $21.5$ $29.9$ $19.4$ $32$ $95\%$ $68\%$ $13.5\%$ $13.5\%$ We know the lifespans are normally distributed with an average lifespan of $25.7$ years. We know the standard deviation is $2.1$ years, so one standard deviation below the mean is $23.6$ years and one standard deviation above the mean is $27.8$ years. Two standard deviations below the mean is $21.5$ years and two standard deviations above the mean is $29.9$ years. Three standard deviations below the mean is $19.4$ years and three standard deviations above the mean is $32$ years. We are interested in the probability of a tiger living between $23.6$ and $29.9$ years. The empirical rule (or the 68-95-99.7 rule) tells us that $95\%$ of the tigers will have lifespans within 2 standard deviations of the average lifespan. It also tells us that $68\%$ of the tigers will have lifespans within 1 standard deviation of the mean. The probability of a particular tiger living between $23.6$ and $29.9$ years is ${68\%} + \color{orange}{13.5\%}$, or $81.5\%$.